U.W. Bangor - School of Informatics - Mathematics Preprints 1996

Pattern Recognition and Fuzzy Systems

On the equivalence between fuzzy and statistical classifiers

Abstract:

We show the equivalence between fuzzy systems for classification and
two nonparametric techniques for pattern recognition: Parzen's
classifier and the nearest neighbor rule. This equivalence has been
vastly implied without being precisely proved. We define a fuzzy
if-then system for classification and derive the conditions under
which it coincides with the above techniques. The equivalence is based
on the following correspondence:
(1) Every reference vector in the data set corresponds to a fuzzy
rule, e.g., the premise part of RULE_k means "is_like_Xk",
where Xk is the k-th element of the reference set (set of
prototypes). The firing strength of RULE_k for an unlabeled
vector x (viz. R_k(x)) is interpreted as a measure of how
similar x is to Xk.
(2) Instead of the usual clauses for the features, e.g., , the clauses become, e.g., , where
Xk(1) is the value of the first feature of the k-th prototype.

Published in:

International Journal of Uncertainty, Fuzziness, and Knowledge- Based Systems
4.3 (1996) 245-253

Fuzzy aggregation of multiple classification decisions

Abstract:

We study some aggregation techniques for multiple classifier
systems. Given an unlabeled object, the first-level classifiers yield
fuzzy decisions in the form of degrees of support for each class to be
the true one for that object. These values are not necessarily
interpreted as posterior probabilities. We use an aggregation operator
based on degree of consensus between the classifiers. The higher the
consensus, the stronger the committee decision (for or against) given
class. Using an acceptance-rejection plot and a small real data set
from neonatal medicine we compared the performance of the aggregation
operator with that of the following aggregation operators:

minimum

maximum

second minimum

second maximum

competition jury

simple average

geometric mean

In general, the consensus based fuzzy aggregation operator led to
better results.

Published in:

A fuzzy consensus aggregation operator

Abstract:

We propose an aggregation operator for expert opinions expressed as
real numbers in the unit interval. These can be interpreted as the
expert confidence in a certain hypothesis. An example is a pool of
classifiers that produce estimates of the posterior probability of an
unlabeled object coming from a certain class. The idea of the operator
is to strengthen the support (for or against the hypothesis) if the
experts agree. We define an axiomatic framework for the aggregation
operator based on this rationale, and suggest several aggregation
formulas. The proposed operator can be used in systems with a
refuse-to-decide option. We illustrate this on an acceptance-rejection
plot with a small data set from neonatology.

Published in:

Prototype knowledge extraction from data using RBF networks

Abstract:

In this paper knowledge-based pattern classification is
considered. Instead of classical fuzzy if-then rules we suggest using
a small reference set of prototypes. The classifier is a
radial-basis-function (RBF) network using the prototype set as
centers. A comparison is drawn with a fuzzy if-then system of the same
size: ANFIS configuration with the same number of rules as the number
of prototypes. Experiments with the two-spirals data show that RBF
classifier makes better use of data than the fuzzy system, i.e. higher
classification accuracy has been achieved with the RBF
classifier. Along with this, keeping the number of prototypes small,
we preserve a certain level of transparency of the RBF classifier,
which has been the most admired feature of fuzzy systems.

Published in:

An intuitionistic fuzzy RBF network

Abstract:

A radial basis function (RBF) network is considered with activation
functions taking highly nonsymmetric form, specific for each
kernel. The representation of the function is inspired by
ntuitionistic fuzzy set theory: every hidden node has a specific
function for activation and another one for restraining. This
flexibility aims at representation of complex classification
boundaries with fewer hidden nodes. The "price" of this is the need
for a special training algorithm. We use simulated annealing. An
illustration example with the two-spirals data is presented.

Published in:

An RBF network with tunable function shape

Abstract:

We propose a radial basis function network with tunable function
shape. Instead of the squared Euclidean distance in the power of the
exponent of the basis function, we suggest to use an L_p norm with
tunable p. We use simulated annealing for training the network. Some
results with the two-spirals data are presented.